Question: Simplify to lowest terms. $\dfrac{12}{30}$
Explanation: There are several ways to tackle this problem. What is the greatest common factor (GCD) of 12 and 30? $12 = 2\cdot2\cdot3$ $30 = 2\cdot3\cdot5$ $\mbox{GCD}(12, 30) = 2\cdot3 = 6$ $\dfrac{12}{30} = \dfrac{2 \cdot 6}{ 5\cdot 6}$ $\hphantom{\dfrac{12}{30}} = \dfrac{2}{5} \cdot \dfrac{6}{6}$ $\hphantom{\dfrac{12}{30}} = \dfrac{2}{5} \cdot 1$ $\hphantom{\dfrac{12}{30}} = \dfrac{2}{5}$ You can also solve this problem by repeatedly breaking the numerator and denominator into common factors. For example: $\dfrac{12}{30}= \dfrac{2\cdot6}{2\cdot15}= \dfrac{2\cdot 3\cdot2}{2\cdot 3\cdot5}= \dfrac{2}{5}$